Cambridge IGCSE Mathematics 0580 — 2010 Oct/Nov Paper 3 · Variant 3

1 For 10 Examiner's Use 9 8 7 6 Frequency 5 4 3 2 1 0 0 1 2 3 4 5 6 Number of children The number of children in each of 40 families was recorded. The bar chart shows the results. (a) Complete the frequency table. Number of children 0 1 2 3 4 5 6 Frequency 4 6 [3] (b) Find (i) the mode, Answer(b)(i) [1] (ii) the median, Answer(b)(ii) [2] (iii) the mean. For Examiner's Use Answer(b)(iii) [3] (c) A pie chart showing the information has been started. (i) Calculate the angles of the sectors for 3 and 4 children. Answer(c)(i) , [3] (ii) Complete the pie chart accurately. 1 child 2 children 0 children 6 children 5 children [1]

Mark scheme: Qu. Answers Mark Part Marks 1 (a) 10, 9, 5, 5, 1 3 B2 for 4 correct, B1 for 3 correct (b) (i) 2 1 (ii) 2.5 2 M1 for evidence of finding mid-value of 20 pieces of data (iii) 2.6 3 M1 for evidence of ∑fx then M1dep for ÷ 40 (c) (i) 81 or 45 2ft ft their 9 or their 5 M1 for their 9 or their 5 ÷ 40 × 360 45 or 81 1ft Correct or ft 126 – their first angle (ii) Correct angles of 81° and 45° 1ft ft only if add up to 126

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2 Eduardo lives in Argentina and travels to Uruguay for a holiday. For Examiner's (a) His flight from Buenos Aires to Montevideo takes 55 minutes. Use The plane departs at 17 35. (i) Write down the arrival time. Answer(a)(i) [1] (ii) The distance between Buenos Aires and Montevideo is 230 km. Calculate the average speed of the plane. Answer(a)(ii) km/h [3] (b) At the airport, Eduardo changed some Argentine pesos (ARS). He received 9121 Uruguay pesos (UYU). (i) The exchange rate was ARS 1 = UYU 6.515. Calculate how many Argentine pesos Eduardo changed. Answer(b)(i) ARS [2] (ii) Eduardo spent 1890 Uruguay pesos on meals. Calculate this as a percentage of the UYU 9121. Answer(b)(ii) % [1] (iii) At the end of his holiday, Eduardo has UYU 610 remaining. He changes this into Argentine pesos when the exchange rate is UYU 1 = ARS 0.149. Calculate how much Eduardo receives in Argentine pesos. Give your answer to the nearest whole number. Answer(b)(iii) ARS [2]

Mark scheme: 2 (a) (i) 18 30 oe 1 (ii) 251 (250.9…) 3 M1 for distance ÷ time (any units) and M1 for 55 ÷ 60 oe (b) (i) 1400 2 M1 for 9121 ÷ 6.515 (ii) 20.7(2…) 1 (iii) 91 2 B1 for 90.89 or 90.9 or 90.8 or 610 × 0.149 or B1 (indep) for correct rounding to integer if from a decimal −5 

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3 For y Examiner's Use 12 11 10 9 8 7 6 G H 5 4 3 F I 2 1 x –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 –1 –2 –3 (a) Describe fully the single transformation that maps (i) flag F onto flag G, Answer(a)(i) [2] (ii) flag F onto flag H, Answer(a)(ii) [2] (iii) flag F onto flag I. Answer(a)(iii) [3] (b) On the grid, draw (i) the reflection of flag F in the y-axis, [2] (ii) the enlargement of flag F, centre (0, 0) and scale factor 4. [2]

Mark scheme:  5  3 (a) (i) Translation   1, 1  3  (ii) Reflection in line y = 4 1, 1 Line can be labelled on diagram (iii) Rotation, (2, 2.5), 180° or half- 1, 1, 1 Centre could be labelled on diagram turn (b) (i) Correct reflection in y-axis 2 SC1 for reflection in x-axis (ii) Correct enlargement, (0, 0), 2 SC1 for any enlargement centre (0, 0) or factor 4 factor 4 IGCSE – October/November 2010 0580 33

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4 For North Examiner's Use North NOT TO C SCALE 75 m B 200 m North A Dariella walks 200 m from A to B. She then turns through 90° and walks 75 m from B to C. (a) Calculate (i) the distance AC, Answer(a)(i) m [2] (ii) angle CAB. Answer(a)(ii) Angle CAB = [2] (b) The bearing of B from A is 065°. Find the bearing of (i) C from A, Answer(b)(i) [1] (ii) A from C, Answer(b)(ii) [1] (iii) C from B. Answer(b)(iii) [2]

Mark scheme: 4 (a) (i) 214 (213.6…) 2 M1 for 752 + 2002 (ii) 20.6 or (20.55 – 20.56) 2 M1 for tan = 75/200 or sin = 75/their (i) or cos = 200/their (i) (b) (i) (0)44 ((0)44.4…) 1ft B1 65 – their (a)(ii) if < 65 (ii) 224 (224.4…) 1ft 180 + their (b)(i) (iii) 335 2 B1 for 65 below B or 25 above B, may be on diagram

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5 For C Examiner's Use D B A The diagram shows a quadrilateral ABCD. (a) Using a straight edge and compasses only, construct (i) the perpendicular bisector of AB, [2] (ii) the bisector of angle ADC. [2] (b) Draw accurately the locus of points, inside the quadrilateral, that are 2 cm from BC. [2] (c) Shade the region, inside the quadrilateral, which is nearer to B than to A and nearer to DC than to DA and more than 2 cm from BC. [1]

Mark scheme: 5 (a) (i) Accurate perpendicular bisector 2 SC1 if accurate without arcs or of AB with arcs accurate bisector of wrong side with arcs (ii) Accurate bisector of angle ADC 2 SC1 if accurate without arcs or accurate bisector of wrong angle with arcs (b) Ruled line 2 cm from and parallel to BC 2 SC1 if not ruled (c) Correct region shaded cao 1 Dependent on at least SC1 in (a)(i), (a)(ii) and (b)

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6 For Examiner's Use NOT TO SCALE 8 cm D C 6 cm 20 cm A 12 cm B The diagram shows a prism of length 20 cm. The cross-section of the prism is a trapezium, ABCD, with AB parallel to DC. AB = 12 cm, DC = 8 cm and the perpendicular distance between AB and DC is 6 cm. (a) Calculate (i) the area of the trapezium ABCD, Answer(a)(i) cm2 [2] (ii) the volume of the prism. Answer(a)(ii) cm3 [1] (b) The prism is solid and made of brass. For Examiner's (i) One cubic centimetre of brass has a mass of 8.5 grams. Use Calculate the mass of the prism. Give your answer in kilograms. Answer(b)(i) kg [2] (ii) Brass costs $2.26 for one kilogram. How much will the brass cost to make this prism? Give your answer correct to 2 decimal places. Answer(b)(ii) $ [2]

Mark scheme: 6 (a) (i) 60 2 M1 for full method for area with correct values (ii) 1200 1ft ft their (i) × 20 (b) (i) 10.2 2ft SC1 for figs 102 or M1 for (a)(ii) × 8.5 ÷ 1000 ft their (a)(ii) × 8.5 ÷ 1000 and SC in same way (ii) 23.05 2ft ft their (b)(i) × 2.26 M1 for 23.052 or 23.1 or (b)(i) × 2.26 or B1ind for correctly rounding to 2 dp an answer with more than 2 dp

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7 Alex has d dollars to spend. For He buys a book which costs $9 less than 2 times d. Examiner's Use (a) Write down an algebraic expression, in terms of d, for the cost of the book. Answer(a) $ [2] (b) The actual cost of the book is $7.80. Find the value of d. Answer(b) d = [2] (c) How much does Alex have left after buying the book? Answer(c) $ [1]

Mark scheme: 7 (a) 2d – 9 2 SC1 for 9 – 2d (b) 8.4(0) 2 M1 for their (a) = 7.8(0) (c) 0.6(0) 1ft ft their (b) – 7.80, only if positive

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8 The area, A, of a sector of a circle of radius r is given by the formula below. For Examiner's Use π r 2 A = 5 (a) Calculate the area when the radius is 7.5 cm. Answer(a) cm2 [2] (b) Make r the subject of the formula. Answer(b) r = [3] (c) Calculate r when A = 4.8 cm2. Answer(c) r = cm [2]

Mark scheme: 8 (a) 35.3 art 2 M1 for substituting r = 7.5 in formula 5 A (b) 3 M1 for correctly multiplying by 5 π M1 for correctly dividing by π M1 for correctly taking a square root (c) 2.76 art cao 2 M1 for substituting 4.8 in their (b) or if working backwards from original formula, substituting and reaching r2 = 5 × 4.8 ÷ π IGCSE – October/November 2010 0580 33

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9 (a) (i) Complete the table for y = 12 – x2. For Examiner's Use x 0 1 2 3 4 y 12 11 – 4 [2] (ii) On the grid, draw the graph of y = 12 – x2 for 0 Y x Y 4. y 12 11

Mark scheme: 9 (a) (i) 8, 3 1, 1 (ii) 5 points correctly plotted 2ft P1 for 4 correct points ft Smooth curve through their 5 1 points (iii) 3.4 Y x Y 3.6 1ft ft their intersection with x-axis (b) (i) 3, 2, 1.5 1, 1, 1 B1 each (ii) 8 points correctly plotted 2ft P1 for 6 or 7 points Smooth branch of rectangular 1 hyperbola through 12 points (c) (1 < x Y 1.2, 10.6 Y y < 11) 1ft ft to same accuracy intersections of their two (2.6 Y x < 3, 4.2 Y y Y 4.5) 1ft graphs

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11 (a) (i) For Examiner's 0, 1, 1, 2, 3, 5, 8, …. Use This sequence has the rule: After the first two terms, any term is the sum of the two previous terms. The first two terms are 0 and 1, the 3rd term is 0 + 1 = 1, the 4th term is 1 + 1 = 2, the 5th term is 1 + 2 = 3 and so on. Show that the 8th term is 13. Answer(a)(i) [1] (ii) Each of the following sequences have the same rule as part (a)(i). For each sequence write down the missing terms. 2, 5, 7, , [1] 4, 3, 7, , [1] 5, 2, , [1] 0, , 3, [1] 1, , , 9, [1] , , 5, 7 [1] (b) For the following sequences find the next term and the n th term. (i) 1, 3, 5, 7, 9, n th term = [3] (ii) 1, 4, 9, 16, 25, n th term = [2] 1 1 1 1 (iii) 1, , , , , n th term = [2] 2 3 4 5

Mark scheme: 11 (a) (i) 5 + 8 (= 13) 1 (ii) 12, 19 1 10, 17 1 7, 9 1 3, 6 1 4, 5 1 3, 2 1 (b) (i) 11 1 2n – 1 2 B1 for 2n ± k or jn – 1 (j ≠ 0) (ii) 36 n2 1, 1 1 1 (iii) 1, 1 6 n

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